Variational Calculation for Large Bipolarons in Arbitrary Dimensions

The calculation model of the large bipolaron binding energy proposed by Verbist et al. is extended to arbitrary dimensions including fractal dimensions. It is found that the fractal dimension D = 1.25 corresponds to the lowest critical coupling constant α_c = 1.9, D = 1.73 corresponds to the highest critical ratio of dielectric constants η_c = 0.163, and when D ≤ 1.145 bipolarons can not exist for any coupling constants and ratios of dielectric constants.